I use package-private
classes and methods when I want to hide implementation details from users (and other classes) outside the package.
For example if I have an interface and a factory class that creates instances of that interface, I may have the implementation class as a separate file but mark it package-private so others can not use it, nor will it clutter the JavaDoc (if javadoc set to only show public).
If you seal your jar file, package-private methods can also help restrict who can access these methods. If a method is public or protected, subclasses can still see and call that method even if it's in a different package. (Unsealed jars allow anyone to make classes in your packages so they will get access to package-private or protected methods)